Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
public class A {
    
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        Vector<Long> v = new Vector<Long>();
        
        for (int i = 1;; i++) {
            long m = i * (i + 1) / 2;
            if (m >= n) {
                break;
            } else {
                v.add(m);
            }
        }
        for (int i = 0; i < v.size(); i++) {
            long complement = n - v.get(i);       
            long r = Collections.binarySearch(v, complement);
            if (r >= 0) {
                System.out.println("YES");           
                System.exit(0);
            }          
        }
        System.out.println("NO");
    }

}